HW 4

Due Dec 7, 2011

Sysplotter code is here

GUI and configuration documentation here and here

• 1. Create a matlab function that outputs the local connection for a three-link low Reynolds number swimmer with unit body length, using the middle-link coordinate system. (hint: working in symbolic variables, then using the command "matlabFunction" is a good way to go).
• 2. Incorporate this local connection function into a system configuration file for use in sysplotter, with a plotting range of ± 2.5 radians on each link
• 3. Plot the connection vector fields for the original and optimized coordinates. Qualitatively describe how they differ. (hint: looking at the gradBeta plots may help)
• 4. Plot the displacement history, BVI and cBVI points for a circular gait with a radius of 1.5 radians, using both the original and optimized coordinates.
• 5. Two common strokes used as benchmarks in studying three-link systems are simple circular strokes (sinusoidal oscillations of the joints) and Purcell strokes (boxes in the shape space, for which each joint moves only while the other is fixed). For both circular and Purcell strokes, in both the original and optimal coordinates
  • a. Find the magnitude of net displacement for a range of gaits with amplitudes between ±0.125 and ±2.25 radians
  • b. Find the BVI and cBVI values for these gaits, and describe their rate of divergence between their magnitudes and the net displacement as the amplitudes increase.
  • c. Find the ranges of the displacement loci for these gaits (in terms of the radians spanned by the resulting arcs). Describe how these loci grow with gait amplitude. Compare the spans of these arcs with the span of angles swept by the body frame during execution of the gait.